Not Between in these date

I would any day suggest to use a combination of two filters rather than using between of any such related operator. 
You can build a logical expression and then add two filters in it. 

1. Filter 1 - Less than Oct 1
2. Filter 2 - Greater than Oct 5

Use the same rule input as the value for both of these filter. That way, you should be able to filter the data. 

I would any day suggest to use a combination of two filters rather than using between of any such related operator. 
You can build a logical expression and then add two filters in it. 

1. Filter 1 - Less than Oct 1
2. Filter 2 - Greater than Oct 5

Use the same rule input as the value for both of these filter. That way, you should be able to filter the data.